Understanding the Mole Concept
In chemistry, the mole is a fundamental unit used to measure the amount of substance. Just as a "dozen" refers to 12 items, a "mole" refers to $6.022 \times 10^{23}$ particles (atoms, molecules, or ions). This is known as Avogadro's number.
To bridge the gap between the mass of a substance (which we can weigh on a scale) and the number of particles (which are too small to count), we use the Molar Mass.
The Formula
The relationship between mass ($m$), molar mass ($M$), and the number of moles ($n$) is given by the formula:
$$n = \frac{m}{M}$$
Where:
- $n$ = number of moles (mol)
- $m$ = given mass (g)
- $M$ = molar mass of the element (g/mol)
Solving the Problem: 15g of Zinc
Question: How many moles of atoms are contained in 15 g of Zn?
Step 1: Identify the given information
- Mass ($m$) = $15\text{ g}$
- Element = Zinc (Zn)
Step 2: Find the molar mass
From the periodic table, the atomic mass of Zinc (Zn) is approximately $65.38\text{ g/mol}$. For most chemistry calculations, rounding to $65.4\text{ g/mol}$ is common and acceptable.
Step 3: Apply the formula
Using our formula $n = \frac{m}{M}$:
$$n = \frac{15\text{ g}}{65.38\text{ g/mol}}$$
Step 4: Calculation
$$n \approx 0.229\text{ mol}$$
Conclusion
By following this simple process, we find that 15 grams of Zinc contains approximately 0.229 moles of atoms.
Key Takeaways:
- Always identify the molar mass: You can find this on the periodic table as the number under the element's symbol.
- Check your units: Ensure your mass is in grams. If it is in milligrams, convert to grams first.
- Conceptual check: Since 15g is significantly less than the molar mass of Zn (~65g), it makes sense that our answer is less than 1 mole.